Semi-inclusive DIS Research Articles

Study of transverse momentum dependent distributions from polarised Drell-Yan at COMPASS

The Parton Distributions Functions (PDFs) and the spin structure of the nucleon are studied by the COMPASS experiment at CERN. The transverse momentum dependent (TMD) PDFs of the proton will be accessed via Drell-Yan (DY) dimuon production in negative pion collisions on a NH 3 transversely polarised target. From this measurement the dimuon azimuthal asymmetries will be extracted, that can be related to 4 TMDs known as transversity, pretzelosity, Sivers and Boer-Mulders. The latter 2 TMDs are time-reversal odd distributions and are expected to change their sign when compared with the ones obtained from Semi-Inclusive Deep Inelastic Scattering, also studied in COMPASS. We aim at performing the first polarised DY measurement starting in 2014.

Polarised Drell-Yan measurements at COMPASS-II

The spin structure of the nucleon and its Parton Distribution Functions (PDFs) are important topics studied by the COMPASS experiment at CERN. So far, the transverse momentum dependent PDFs (TMD PDFs) of the proton and deuteron have been studied in Semi-Inclusive Deep Inelastic Scattering (SIDIS). The Drell-Yan (DY) process is a complementary way to access the TMD PDFs, using a transversely polarised target. Studying the angular distributions of dimuons from the DY events produced in the collisions of a π− beam with 190 GeV/c momentum off a transversely polarised proton target (NH3) we are able to extract the azimuthal spin asymmetries, which are generated by 4 out of the 8 TMD PDFs needed to describe the nucleon structure at leading order QCD. The expected sign change in Sivers and Boer-Mulders functions when accessed from DY and SIDIS will be checked [1]. The opportunity to study, in the same experiment, the TMD PDFs from both SIDIS and DY processes is unique at COMPASS. The COMPASS II Proposal [2] was approved by CERN including one year for polarised DY measurements; the beginning of the DY data taking is scheduled for 2014. The feasibility of the measurement was proven by several beam tests performed so far.

The TMD program at CLAS and CLAS12

Transverse-momentum-dependent parton distributions (TMDs) are crucial ingredients for a complete understanding of the dynamics of confined par-tons. They allow for a 3-dimensional description of the nucleon in momentum space, and could provide insights into the yet unmeasured quark orbital angular momentum. At CLAS several TMDs are explored in Fourier analysis of azimuthal asymmetries measured in semi-inclusive DIS. An overview of the main CLAS results as well as selected CLAS12 projected results is presented.

EXPERIMENTAL STUDY OF SINGLE SPIN ASYMMETRIES AND TMDs

Single Spin Asymmetries and Transverse Momentum Dependent (TMD) distribution study has been one of the main focuses of hadron physics in recent years. The initial exploratory Semi-Inclusive Deep-Inelastic-Scattering (SIDIS) experiments with transversely polarized proton and deuteron targets from HERMES and COMPASS attracted great attention and lead to very active efforts in both experiments and theory. A SIDIS experiment on the neutron with a polarized 3 He target was performed at JLab. Recently published results as well as new preliminary results are shown. Precision TMD experiments are planned at JLab after the 12 GeV energy upgrade. Three approved experiments with a new SoLID spectrometer on both the proton and neutron will provide high precision TMD data in the valence quark region. In the long-term future, an Electron-Ion Collider (EIC) as proposed in US (MEIC@JLab and E-RHIC@BNL) will provide precision TMD data of the gluons and the sea. A new opportunity just emerged in China that a low-energy EIC (1st stage EIC@HIAF) may provide precision TMD data in the sea quark region, complementary to the proposed EIC in US.

Flavor dependent azimuthal asymmetries in unpolarized semi-inclusive DIS at HERMES

The azimuthal cosϕh and cos2ϕh modulations of the distribution of hadrons produced in unpolarized semi-inclusive deep-inelastic scattering of electrons and positrons off hydrogen and deuterium targets have been measured in the hermes experiment. For the first time these modulations were determined in a 4-Dimensional kinematic space for positively and negatively charged pions and kaons separately, as well as for unidentified hadrons. These azimuthal dependences are sensitive to the transverse motion and polarization of the quarks within the nucleon via, e.g., the Cahn, Boer-Mulders and Collins effects.

QCD analysis of the semi-inclusive COMPASS and HERMES data

The first moments of polarized valence parton distribution functions truncated to the wide Bjorken x region 0.004 < x < 0.7 are directly (without any fitting procedure) extracted in the NLO QCD from combined semi-inclusive DIS data of COMPASS and HERMES collaborations. Two scenarios for fragmentation functions are considered. Applying the proposed original procedure to these results we estimate the contributions of sea u and d quarks to the proton spin, which turn out to be simply zero within the errors.

Overview of recent results from the HERMES experiment

HERMES has taken a wealth of deep-inelastic scattering (DIS) data using the 27.6 GeV polarized lepton beam at HERA and various pure gas targets, both unpolarized and polarized, which opened the door to several unique results. Among them are the first evidences for the naive-T-odd Sivers and Collins effects but also the recent first measurements of azimuthal modulations in the unpolarized semi-inclusive DIS cross section for charged kaons and pions and of beam-helicity asymmetries in exclusive leptoproduction of real photons using recoil-proton detection. An overview of HERMES results is given with emphasis on the exploration of the three-dimensional structure of the nucleon.

Beam spin asymmetries of charged and neutral pion production in semi-inclusive DIS

We present a study on the beam single spin asymmetries $A_{LU}^{\sin\phi_h}$ of $\pi^+$, $\pi^-$ and $\pi^0$ production in semi-inclusive deep inelastic scattering process, by considering Collins effect and the $g^\perp D_1$ term simultaneously. We calculate the twist-3 distributions $e(x, \bm k_T^2)$ and $g^\perp(x,\bm k_T^2)$ for the valence quarks inside the proton in a spectator model. We consider two different options for the form of diquark propagator, as well as two different choices for the model parameters in the calculation. Using the model results, we estimate the beam spin asymmetries $A_{LU}^{\sin\phi_h}$ for the charged and neutral pions and compare the results with the measurement from the HERMES Collaboration. We also make predictions on the asymmetries at CLAS with a $5.5 \,\textrm{GeV}$ beam using the same model results. It is found that different choices for the diquark propagator will not only lead to different expressions for the distribution functions, but also result in different sizes of the asymmetries. Our study also shows that, although the spectator model calculation can describe the asymmetries for certain pion production in some kinematic regions, it seems difficult to explain the asymmetries of pion production for all three pions in a consistent way from the current versions.

Single-spin asymmetries in semi-inclusive deep inelastic scattering and Drell-Yan processes

We examine in detail the diagrammatic mechanisms which provide the change of sign between the single transverse spin asymmetries measured in semi-inclusive deep inelastic scattering (SIDIS) and in the Drell-Yan process (DY). This asymmetry is known to arise due to the transverse spin dependence of the target proton combined with a $T$-odd complex phase. Using the discrete symmetry properties of transverse spinors, we show that the required complex phase originates in the denominators of rescattering diagrams and their respective cuts. For simplicity, we work in a model where the proton consists of a valence quark and a scalar diquark. We then show that the phases generated in SIDIS and in DY originate from distinctly different cuts in the amplitudes, which at first appears to obscure the relationship between the single-spin asymmetries in the two processes. Nevertheless, further analysis demonstrates that the contributions of these cuts are identical in the leading-twist Bjorken kinematics considered, resulting in the standard sign-flip relation between the Sivers functions in SIDIS and DY. Physically, this fundamental, but yet untested, prediction occurs because the Sivers effect in the Drell-Yan reaction is modified by the initial-state ``lensing'' interactions of the annihilating antiquark, in contrast to the final-state lensing which produces the Sivers effect in deep inelastic scattering.

Magnetic System for the CLAS12 Proposal

The conceptual design of a magnetic system for an experiment to measure the transverse spin effects in semi-inclusive Deep Inelastic Scattering (SIDIS) at 11 GeV with a transversely polarized target using the CLAS12 detector at Jefferson Lab is presented. A proposal has been submitted to study spin azimuthal asymmetries in SIDIS using an 11-GeV polarized electron beam from the upgraded CEBAF facility and the CLAS12 detector equipped with a transversely polarized target. The main focus of the experiment will be the measurement of transverse target single and double spin asymmetries in the reaction ep↑ → ehX, where e is an electron, p↑ is transversely polarized proton, h is a meson (e.g., a pion or a kaon) and X is the undetected final state. The details of the conceptual design of the shielding magnetic system and transverse dipole are reported.

Polarized semi-inclusive electroweak structure functions at next-to-leading-order

We present a next-to-leading order (NLO) computation of the full set of polarized and unpolarized electroweak semi-inclusive DIS (SIDIS) structure functions, whose knowledge is crucial for a precise extraction of polarized parton distributions. We focus on the phenomenology of the polarized structure functions for the kinematical conditions that could be reached in an Electron-Ion-Collider. We show that the NLO corrections are sizeable, particularly in the small-$x$ range. We test the sensitivity of these structure functions on certain quark distributions and compare it to the situation of inclusive DIS and electromagnetic SIDIS.

Experimental Program of the Future COMPASS-II Experiment at CERN

Over the last decade the COMPASS experiment has successfully obtained precise results on nucleon structure and hadron spectroscopy, with statistical errors much lower than previously reported. Recently, the new COMPASS-II program, focused on the study of a more complete nucleon description, was approved by CERN. The goal of the program is to access the nucleon structure beyond the collinear approxi-mation, including the quark intrinsic transverse momentum distributions, which are described by the Transverse Momentum Dependent (TMD) Parton Distribution Functions (PDFs) and by Generalised Parton Distributions (GPDs). The COMPASS collaboration proposes to measure the TMD PDFs, for the first time, via the polarised Drell-Yan process. The results will be complementary to those already obtained in polarised Semi-Inclusive Deep Inelastic Scattering (SIDIS). The GPDs can be accessed using deeply virtual Compton scattering and hard exclusive meson production using an unpolarised hydrogen target in a kinematic region not yet covered by any existing experiment. Also unpolarised SIDIS will be studied, by improving the knowledge of the strange quark PDF and obtaining the kaon fragmentation functions. Another topic covered in this COMPASS-II program is the measurement of the pion and kaon polarisabilities using the Primakoff reaction, which corresponds to a test of the chiral perturbative theory.

Probing the nucleon structure with SIDIS at Jefferson Lab.

In recent years, measurements of azimuthal moments of polarized hadronic cross sections in hard processes have emerged as a powerful tool to probe nucleon structure. Many experiments worldwide are currently trying to pin down various effects related to nucleon structure through Semi-Inclusive Deep-Inelastic Scattering (SIDIS). Azimuthal distributions of final-state particles in semi-inclusive deep inelastic scattering, in particular, are sensitive to the orbital motion of quarks and play an important role in the study of Transverse Momentum Dependent parton distribution functions (TMDs) of quarks in the nucleon. The CLAS spectrometer, installed in Hall-B at Jefferson Lab, has collected semi-inclusive data using the CEBAF 6 GeV polarized electron beam on polarized solid NH3 and ND3 targets. An overview of these measurements is presented.

Symmetry breaking effect on determination of polarized and unpolarized parton distributions

We perform a new extraction for unpolarized and polarized parton distribution functions considering a flavor decompositions for sea quarks and applying very recent deep inelastic scattering (DIS) and semi inclusive deep inelastic scattering (SIDIS) data in the fixed flavor number scheme (FFNS) framework. In the new symmetry breaking scenario the light quark and antiquark densities are extracted separately and new parametrization forms are determined for them. The heavy flavors contribution, including charm and bottom quarks, are also taken to be account for unpolarized distributions.

Calculation of Transverse-Momentum-Dependent Evolution for Sivers Transverse Single Spin Asymmetry Measurements

The Sivers transverse single spin asymmetry (TSSA) is calculated and compared at different scales using the transverse-momentum-dependent (TMD) evolution equations applied to previously existing extractions. We apply the Collins-Soper-Sterman (CSS) formalism, using the version recently developed by Collins. Our calculations rely on the universality properties of TMD functions that follow from the TMD-factorization theorem. Accordingly, the nonperturbative input is fixed by earlier experimental measurements, including both polarized semi-inclusive deep inelastic scattering (SIDIS) and unpolarized Drell-Yan (DY) scattering. It is shown that recent preliminary COMPASS measurements are consistent with the suppression prescribed by TMD evolution.

Global fitting of single spin asymmetry: An attempt

We present an attempt of global analysis of Semi-Inclusive Deep Inelastic Scattering (SIDIS) $\ell p^\uparrow \to \ell' \pi X$ data on single spin asymmetries and data on left-right asymmetry $A_N$ in $p^\uparrow p \to \pi X$ in order to simultaneously extract information on Sivers function and twist-three quark-gluon Efremov-Teryaev-Qiu-Sterman (ETQS) function. We explore different possibilities such as node of Sivers function in $x$ or $k_\perp$ in order to explain "sign mismatch" between these functions. We show that $\pi^\pm$ SIDIS data and $\pi^0$ STAR data can be well described in a combined TMD and twist-3 fit, however $\pi^\pm$ BRAHMS data are not described in a satisfactory way. This leaves open a question to the solution of the "sign mismatch". Possible explanations are then discussed.

Transverse-momentum-dependent fragmentation and quark distribution functions from the Nambu–Jona-Lasinio–jet model

Using the model of Nambu and Jona-Lasinio to provide a microscopic description of both the structure of the nucleon and of the quark to hadron elementary fragmentation functions, we investigate the transverse momentum dependence of the unpolarized quark distributions in the nucleon and of the quark to pion and kaon fragmentation functions. The transverse momentum dependence of the fragmentation functions is determined within a Monte Carlo framework, with the notable result that the average $P_\perp^2$ of the produced kaons is significantly larger than that of the pions. We also find that $<P_\perp^2>$ has a sizable $z$ dependence, in contrast with the naive Gaussian ansatz for the fragmentation functions. Diquark correlations in the nucleon give rise to a non-trivial flavor dependence in the unpolarized transverse momentum dependent quark distribution functions. The $<k_T^2>$ of the quarks in the nucleon are also found to have a sizable $x$ dependence. Finally, these results are used as input to a Monte Carlo event generator for semi-inclusive deep inelastic scattering (SIDIS), which is used to determine the average transverse momentum squared of the produced hadrons measured in SIDIS, namely $<P_T^2>$. Again we find that the average $P_T^2$ of the produced kaons in SIDIS is significantly larger than that of the pions and in each case $\la P_T^2 \ra$ has a sizable $z$ dependence.

Semi-inclusive DIS Experiments Using Transversely Polarized Targets in Hall-A: Current Results and Future Plans

Measurement of single (SSA) and double spin asymmetries (DSA) in semi- inclusive DIS reactions using polarized targets provide a powerful method to probe trans- verse momentum dependent parton distribution functions (TMDs). In particular, the ex- perimentally measured SSA on nucleon targets can help in extracting the transversity and Sivers distribution functions of u and d-quarks. Similarly, the measured DSA are sensitive to the quark spin-orbital correlations, and provide an access to the TMD parton distribu- tion function (g1T ). A recent experiment conducted in Hall-A Jefferson Lab using trans- versely polarized 3 He provide first such measurements on effective neutron target. The measurement was performed using 5.9 GeV beam from CEBAF and measured the target SSA/DSA in the SIDIS reaction 3 He (e, e 0 � � )X. The kinematical range, x = 0.19�0.34, at Q 2 = 1.77�2.73 (GeV/c) 2 , was focused on the valence quark region. The results from this measurement along with our plans for future high precision measurements in Hall-A are presented.

Studying the Sivers and Boer-Mulders Function with Lattice QCD

Transverse momentum dependent parton distribution functions (TMDs) characterize the intrinsic momentum distribution of quarks inside the nucleon. However, they also encode final or initial state interactions of the processes in which they are measured, such as semi-inclusive deep inelastic scattering (SIDIS) or the Drell–Yan process (DY). Consequently certain TMDs are process-dependent and predicted to be equal but opposite in sign for SIDIS and DY. Extending our method on the lattice to non-local operators with U-shaped Wilson lines, we can study these naively time-reversal odd TMDs, in particular the Sivers- and the Boer-Mulders function. We express our results in terms of Fourier-transformed TMDs that appear naturally in the Fourier transformed cross section of, e.g., SIDIS, and in Bessel-weighted asymmetries. We discuss the method, its limitations and preliminary results from an exploratory calculation using lattices generated by the MILC and LHP collaborations.

Transverse target spin asymmetries at COMPASS

COMPASS is a fixed target experiment at the CERN M2 beamline where the nucleon spin structure is investigated using a 160 GeV/c polarized μ+ beam and polarized solid state targets. After taking data in the years 2002–2004 using a transversely polarized 6LiD (deuteron) target, in 2007 and 2010 additional data were collected on a transversely polarized NH3 (proton) target. The measurements of single spin asymmetries in semi-inclusive deep inelastic scattering (SIDIS) on a transversely polarized target are an important part of the COMPASS physics program. They allow to investigate the transversity distribution functions, e.g. coupled to the Collins fragmentation function, as well as transverse momentum dependent distribution functions, like the Sivers distribution function, by measuring azimuthal asymmetries in hadron production.